Random ordinate method for Kinetic models
报告专家：唐敏 教授（上海交通大学）
报告时间：10月12日（星期一） 10:30--11:30
报告地点：数学学院西202
报告摘要：
Kinetic equations are of fundamental importance in a wide range of applications, including rarefied gas dynamics, radiative transfer, plasma transport, and other non-equilibrium phenomena where continuum models are no longer valid. Their broad applicability, however, is accompanied by severe numerical challenges. A central difficulty is their high dimensionality: the unknown depends on both physical space and velocity or angular space, leading to a rapidly growing computational cost. In addition, the solution may lack regularity. Especially in transition regimes or in the presence of discontinuities in boundary conditions or flow fields, the velocity distribution can become strongly anisotropic, develop sharp gradients, or even become discontinuous. Such non-regular features make numerical discretization difficult and often induce the well-known ray effect, i.e., unphysical directional oscillations caused by fixed angular or velocity grids in traditional discrete ordinate and discrete velocity methods.
This talk presents a general approach to angular discretization for kinetic equations. The method introduces randomness or unbiased sampling into the angular/velocity discretization, thereby removing the directional bias of deterministic fixed grids and effectively suppressing ray-effect oscillations, while retaining the general discrete-velocity/discrete-ordinate framework. The proposed strategy is model-independent and broadly applicable. In particular, it is not limited to steady radiative transfer; it is also extended to the BGK equation for rarefied gas flows and possiblely other kinetic models.
专家简介：
马上海交通大学数学学院/自然科学研究院教授，从事与多尺度现象相关的应用数学研究，设计物理、工程问题数值模拟中的多尺度、可并行算法，建立生物系统中不同尺度现象的关联。主持基金委NSAF联合（重点）基金，面上等项目。部分工作被作为合作者国际数学家一小时报告主要内容。2018 年入选国家级青年人才；受邀出任了应用数学重要期刊SIAM- Multiscale Modeling&Simulations, Journal of Mathematical Biology, Kinetic and Related Models, Communications in Mathematical Sciences等期刊编委。
邀请人：唐庆粦
